On the low energy limit of reflection and sticking coefficients in atom surface scattering

The effect of long range van der Waals type potentials (∝ 1/z3) on elastic and inelastic scattering of atoms by solid surfaces is investigated. The elastic scattering is described in terms of the single particle self energy which was introduced already for the description of short range potential scattering. The case of Helium scattering is considered in particular. In this case a perturbation expansion of the self energy is possible. There are at least four important differences as compared to short range forces:1. (in agreement with earlier work of other groups) the WKB approximation leading to an energy independent sticking coefficient at low energies is valid down to energies being four orders of magnitude lower than for short range Morse type potentials.2. Below the range of validity of the WKB approximation the amplitude of the wave function in the attractive well drops to zero (as for short range forces). The simple effective range theory, however, is not applicable. The scattering length diverges logarithmically.3. The effect of scattering resonances also shows up only at energies being four orders of magnitude lower than for short range forces.4. Second order corrections to the inelastic seattering amplitude involve an energy shift which (due to the approximate energy independence of the zero order sticking coefficient) is almost logarithmically divergent at low energies. This leads to an increase of the sticking coefficient with decreasing energy.